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Empirical properties of the variety of a financial portfolio and the single-index model

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  • Fabrizio Lillo
  • Rosario N. Mantegna

Abstract

We investigate the variety of a portfolio of stocks in normal and extreme days of market activity. We show that the variety carries information about the market activity which is not present in the single-index model and we observe that the variety time evolution is not time reversal around the crash days. We obtain the theoretical relation between the square variety and the mean return of the ensemble return distribution predicted by the single-index model. The single-index model is able to mimic the average behavior of the square variety but fails in describing quantitatively the relation between the square variety and the mean return of the ensemble distribution. The difference between empirical data and theoretical description is more pronounced for large positive values of the mean return of the ensemble distribution. Other significant deviations are also observed for extreme negative values of the mean return.

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  • Fabrizio Lillo & Rosario N. Mantegna, 2000. "Empirical properties of the variety of a financial portfolio and the single-index model," Papers cond-mat/0009401, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0009401
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    Cited by:

    1. Gu, Gao-Feng & Zhou, Wei-Xing, 2007. "Statistical properties of daily ensemble variables in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 497-506.
    2. Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N., 2001. "Levels of complexity in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 16-27.
    3. Fabrizio Lillo & Giovanni Bonanno & Rosario N. Mantegna, 2001. "Variety of Stock Returns in Normal and Extreme Market Days: The August 1998 Crisis," Papers cond-mat/0104362, arXiv.org.
    4. Indranil Mukherjee & Amitava Sarkar, 2011. "Complexity, Financial Markets and their Scaling Laws," DEGIT Conference Papers c016_008, DEGIT, Dynamics, Economic Growth, and International Trade.

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